I'm not going to get into this thread, just going to state my opinion and rebuke the big arguments against exotic ownership in the private sector.
No animal should be banned from being owned in the private sector. Limits should be placed as far as the number that may be taken from the wild, and individuals should be entered into a database that keeps track of who has what. That's it. No bans, no impossible hoops to jump through.
Now, to rebut the biggest arguments:
1. "They're wild animals, they belong in the wild!"
Exactly what "wild" are you referring to? The one prowled by poachers, ready to massacre a population to make money? The constantly shrinking fragments of natural habitat, continually being destroyed to make way for human "progress"? The wild that can only support so many animals, that number going down as habitat is cleared? The one where most animals never live to see adulthood? That wild?
The sad truth is that there isn't much wild left for these animals to belong in. Of that, even less is safe from human interference in the form of poaching. There is almost no untouched habitat left, and what little there is has its share of animals, it is full. It's at carrying capacity, so animals in captivity would simply get pushed out. This already happens to many species, and they resort to going through our garbage and asking for handouts. The wild is shrinking, and it is overflowing as is. Without established breeding populations in captivity, many species will simply cease to exist.
2. "Only qualified zoos should keep them!"
The answer is a combination of too little and too much. For starters, the number of zoos and the amount of space each of those zoos has is finite. It's rather limited, actually. Constantly, this argument is used with the presumption that there are enough zoos for these animals to be placed in. How much free space do you actually see at most zoos? How many empty cages? None. On top of that, anyone who has worked at a zoological facility will tell you that the resources they have are actually quite constrained. A lot of money goes into the initial construction of a zoo, but past that they are often left with somewhat little spare cash, as most money goes towards maintaining the animals they have. Most zoos keep animals in enclosures that haven't been renovated since their construction, zoos are not constantly expanding to make room for more animals, they don't have the budget for it. That's why it's such a big deal when it does actually happen. They don't have enough space or money to take in the occasional unwanted pet, what on Earth could lead anyone to believe that zoos and zoos alone have enough resources to sustain a genetically viable captive population of every species that is being driven to extinction? Moving on to the point of too much, zoos manage incredibly diverse collections of animals, so diverse that they can only keep a few of each species. Often only one or two of the larger species, not enough to sustain a healthy captive population. On top of that, zoos increasingly operate with a skeleton crew of generalist keepers, as opposed to a larger number of specialized keepers. What it all boils down to is that each individual species does not receive as much attention as they would otherwise, making successful breeding and advances in husbandry harder to accomplish. The lack of extra funds for enclosure upgrades only compounds this issue.
Enter the private sector. A massive number of specialized individuals, each keeping a smaller collection of often very similar animals. Each has time and funds to devote to their own species, and the flexibility to experiment with and improve husbandry standards. The massive scale of the private sector means that large, genetically diverse populations of captive animals can be maintained, far more than zoos could ever hope to accomplish.
3. "They could escape and hurt someone!"
Firstly, the same applies to zoos. The difference though is that zoo enclosures are often decades old, and not as suited to the animals as enclosures in the private sector. In addition to this, zoos invite thousands of people in every day, whereas in a private collection, the only people coming near the animals are either the owners or friends, who often are as qualified as the owner to deal with these animals, unlike the thousands of ignorant monkeys meandering about zoos who couldn't tell a King Cobra from a Ball Python even if it bit them on the face. Zoos have a far more extensive track record of animal escapes than private keepers do, and there is also the issue of nutjobs trying to get into a cage, who may pose a danger to the animals. That list is even longer in zoos and much shorter in the private arena.
Secondly, the bottom line is that exotic animals account for extremely few fatalities, and almost every one of those is the keeper or a friend/family member. An escaped exotic on a killing spree is less likely to kill you than your bathtub, lightning, or a terrorist attack. Being killed by medical malpractice is more likely than all of those combined.
Using some quick stats off of a Google search, exotic pets account for a grand total of 75 deaths between 1990 and 2011. That comes out to a bit over three and a half deaths each year. Medical malpractice kills 195,000 every year. I'll take my chances with the animals.
4. "The animals are kept in terrible conditions!"
Of course some are. The fact of the matter is that there will always be bad eggs. Some people should not have children, but how many laws do you see introduced to ban people from having kids? While those bad eggs constitute virtually 100% of the media coverage exotic animals receive, it is not the norm. The truth is that very few people buy animals because they want something "cool" to show off to their friend. Those that ask are usually turned down by the seller, and to be honest something like a tiger is not something you can buy on a whim, despite what the media and the animal rights activists will say. Go find me a tiger for sale that someone could buy because they felt like it. Go ahead. If someone is going to go through all the trouble of tracking down and purchasing such an animal (Which would likely take months, or even years) do you really think they are just going to slap it in a chain link kennel and ignore it? No, the vast majority of keepers love their animals, and will do whatever it takes to care for them. Most cases where animals are not cared for properly are cases of misinformation, not lack of interest in the animal's well being. Zoos are guilty of it as much as the private sector is, for that matter. Just ask any experienced monitor keeper.. Zoos are not omnipotent when it comes to animal care, as a matter of fact they are often behind. The people who run zoos are the same as private keepers, just with less flexibility. They are often stuck with husbandry practices several decades old because they're required to follow the approved guidelines, which take large amounts of time and money to modify, even when they clearly do not work. In addition, zoos have to worry about making money, meaning that oftentimes aesthetic appeal to visitors is given priority over the animal's well-being.
We need the private sector, and the animals need it even more.